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Letter
Deciphering Front-Side Complex Formationin S
N
2 Reactions via Dynamics MappingIstvan Szabo, Balazs Olasz, and
Gabor Czako
J. Phys. Chem. Lett., Just Accepted Manuscript • Publication
Date (Web): 09 Jun 2017
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Deciphering Front-Side Complex Formation in SN2
Reactions via Dynamics Mapping
István Szabó*,†, Balázs Olasz‡ and Gábor Czakó*,‡
†Department of Chemistry, King’s College London, London SE1 1DB,
UK
‡Department of Physical Chemistry and Materials Science,
Institute of Chemistry, University of
Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
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ABSTRACT
Due to their importance in organic chemistry the atomistic
understanding of bimolecular
nucleophilic substitution (SN2) reactions shows exponentially
growing interest. In this
publication the effect of front-side complex (FSC) formation is
uncovered via quasi-classical
trajectory computations combined with a novel analysis method
called trajectory orthogonal
projection (TOP). For both F− + CH3Y [Y=Cl,I] reactions the life
time distributions of the F−--
YCH3 front-side complex revealed weakly trapped nucleophiles
(F−). However, only the F− +
CH3I reaction features strongly trapped nucleophiles in the
front-side region of the prereaction
well. Interestingly, both back-side and front-side attack show
propensity to long-lived FSC
formation. Spatial distributions of the nucleophile demonstrate
more prominent FSC formation in
case of the F− + CH3I reaction compared to F− + CH3Cl. The
presence of front-side intermediates
and the broad spatial distribution in the back-side region may
explain the indirect nature of the F−
+ CH3I reaction.
TOC GRAPHICS
KEYWORDS mechanism, nucleophilic substitution, ion-dipole
complex, front-side
intermediate, quasi-classical, trajectory projection, life time,
Nu− capture
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Ion-dipole bimolecular nucleophilic substitution (SN2) is among
the most prevalent reaction
pathways in chemistry and biochemistry.1-6 However, unlike what
is suggested in organic
chemistry textbooks the dynamics of these reactions are quite
complex.7-10 A general overall SN2
reaction can be written as Nu− + CH3Y → CH3Nu + Y−, where Nu−
and Y denote the attacking
nucleophile and the leaving group, respectively. Potential
energy landscape for this family of
reactions is comprised of a central barrier which separates the
pre- and postreaction wells.
According to our current atomistic understanding, reactive
events usually begin with the attack
of the Nu− nucleophile on the methyl side of CH3Y forming
ion-dipole (Nu−--H3CY) and/or
hydrogen-bonded (Nu−--HCH2Y) pre-reaction complexes then the
system goes through the
central transition state [Nu--CH3--Y]−, where synchronously a
new Nu-C bond forms and the C-
Y bond breaks, while the umbrella motion around the sp3 carbon
center inverts the configuration.
At higher translational energies the endothermic H-abstraction
and the front-side attack channels
open. The later pathway leads to retention of the final
configuration, as well as the double-
inversion mechanism revealed by our dynamics simulations8 in gas
phase and recently confirmed
also in aqueous solution.11
Recently, the F− + CH3Cl and F− + CH3I SN2 reactions were probed
with combined crossed-
beam imaging and molecular dynamics simulations providing
interesting clues to the overall
dynamics of SN2 reactions at an atomistic level.9 Both reactions
are highly exothermic and
characterized by a similar potential energy landscape with a
Cs-symmetric H-bonded complex in
the entrance channel together with the traditional close-lying
ion-dipole complex of C3v
symmetry connected by a low-barrier transition state. Despite of
these similarities, the dynamics
of the two reactions showed substantial differences, which
indicated the influence of the leaving
group in the SN2 mechanism even in the entrance channel. In case
of the F− + CH3Cl SN2
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reaction we have found that at low collision energies the
indirect mechanism dominates, whereas
at higher collision energies the reaction mainly occurs via the
direct rebound mechanism.9,12 In
contrast, for the F− + CH3I SN2 reaction a major contribution of
the indirect mechanism to the
total cross-section was observed at all collision energies
investigated supported by the product
velocity, scattering angle and product internal energy
distributions.9,12,13 These unexpected
qualitative differences were putatively explained based on the
differences in dipole moments
which might affect the orientation of the reactants. However,
the observed changes in
mechanism were not completely clarified.9 Very recently, Xie and
Hase envisioned in their
perspective article10 the determining role of the front-side
complexes to suppress back-side attack
and the roundabout mechanism accordingly. Front-side complexes
have been recognized for
assisting in dihalide formation in the F− + CF3Br, F− + CF3I,
and Cl
− + CF3Br reactions.14-16
Detailed unimolecular dynamics with lifetime distributions were
determined for the [CH3--I--
OH]− front-side complex by Hase and co-workers.17 Moreover, FSCs
were proposed to explain
the indirect nature of several prototypical SN2 reactions, e.g.
OH− + CH3I,
17-19 and F− + CH3I,13
but the exact causes of the observed differences in the
mechanism remained unclear. Our aim is
to provide a detailed characterization of the structure and
energetics of the Nu−--YCH3
[Nu=F,Cl,Br,I; Y=Cl,Br,I] front-side complex minima and to
explore the fascinating mechanistic
roles of these intermediate ion-dipole complexes on the example
of the prototypical F−--YCH3
[Y=Cl,I] SN2 reactions. Of particular interest is the time-scale
of the trapping in the front-side
pre-reaction well.
Potential energy surfaces of the Nu− + CH3Y [Nu=F,Cl,Br,I;
Y=Cl,Br,I] reactions feature a
potential energy well in the front-side region, i.e. in close
proximity of the leaving group.
Relative energies of the corresponding minima strongly depend on
the nucleophile and also the
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leaving group. As shown in Figure 1a, the F− + CH3I reaction has
a front-side complex with a
potential energy minimum of −22.8 kcal mol−1, relative to the
reactants, and the equivalent FSC
minimum for the F− + CH3Cl reaction is only −2.7 kcal mol−1,
whereas the corresponding values
on our chemically accurate analytical potential energy surfaces
(PESs) are −22.6 and −3.7 kcal
mol−1, respectively.13 Considering all the possible Nu−--YCH3
[Nu=F,Cl,Br,I; Y=Cl,Br,I] front-
side minima (shown in Figure S1) the [F--ICH3]− has the deepest
minimum, followed by the F−--
BrCH3 and Cl−--ICH3 complexes characterized by a potential
energy minimum of −10.7 and
−9.2 kcal mol−1, respectively. Note that the aforementioned
OH−--ICH3 long-lived intermediate
complex is characterized by an even deeper potential minimum of
−26.1 kcal mol−1, predicted by
DFT based methods.17 (The corresponding value is −24.1 kcal
mol−1 at the CCSD(T)-F12b/aug-
cc-pVTZ(-PP) level of theory.) Regarding the structure of
F−--YCH3 [Y=Cl,I], the F-I bond
length is 0.191 Å longer than the F-Cl distance. The Cl-C/I-C
bond length in F−--YCH3 [Y=Cl,I]
is 0.006/0.077 Å shorter than the corresponding bond in
CH3Cl/CH3I. According to the Natural
Bond Orbital population analysis of F−--YCH3 [Y=Cl,I] the Cl and
I atoms carry a partial charge
of +0.02 and +0.25, respectively, whereas the H atoms carry
+0.16 for both front-side
intermediates. In contrast to the F−--ICH3 ion-dipole complex,
the negative charge is distributed
disproportionately between the F and C atoms of the F−--ClCH3
complex with −0.97 and −0.52,
respectively.
To get insight into the energetics of the front-side attachment
of the F− ion to the methyl-halide
in the entrance channel, the two-dimensional (2D) interaction
potential was calculated by
performing a scan of the PES with YCH3 [Y=Cl,I] fixed in its
equilibrium geometry. From the
2D interaction potentials depicted in Fig. 1c-f we can
distinguish two deep wells for both
reactions, corresponding to the interactions of the Nu−
nucleophile with the –CH3 group and the
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halogens (Y=Cl,I). It is clearly seen, that the back and
front-side complex wells are separated by
a potential-ridge, which intersects the halogen at both limiting
F-C-Y-H dihedral angles (see Fig.
1b). On the –CH3 side, the bottom of the potential energy well
features the collinear ion-dipole
and H-bonded pre-reaction complexes, which strongly influence
the migration of the Nu−
between the BSC and FSC regions of the F−--YCH3 [Y=Cl,I] SN2
reactions.9 In the front-side
region the interaction potentials substantially deviate, due to
the differences in the attraction of
the two halogens. The nature of the complexation in this well is
less well understood. Based on
the shape of the interaction potential we hypothesised that the
potential well in the front-side
region is suitable to capture the approaching nucleophile in
close proximity of the leaving group.
As we know, the trajectories may avoid even the deep potential
minimum,20 thus we cannot rely
solely on the potential energy landscapes. Therefore, we are
proposing an alternative approach,
called trajectory orthogonal projection (TOP) to visualize and
to quantify the nucleophilic attack
in SN2 reactions. Our methodology consists of the following
simple steps: (1) quasi-classical
trajectories are run at a given collision energy covering the
impact parameter (b) range from 0 to
the maximum value of b, where reactive event is likely to occur,
(2) the three-dimensional
positions of the nucleophile in the entrance channel are
orthogonally projected to one- or two-
dimensional subspaces defined by certain atoms of CH3Y, (3) the
distribution of the resulting
positions is obtained by the standard Histogram Binning
technique.21 In fact, the TOP method
aligns the reactive system to subspaces defined with the nuclei
in the CH3Y polyatomic reactant
providing the spatial probability of nucleophilic attack around
CH3Y in a given point of the
subspace. Spatial distributions in the subspaces like the line
through the {Y,C} nuclei, the
{Y,C,H} plane or the plane perpendicular to {Y,C,H} are all very
informative in terms of
mapping the effective dynamics of the system. One should
emphasize that TOP is capable to
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reveal reaction channels which are unlikely to follow the
minimum energy path predicted by the
potential energy landscape.
With analytical potential energy functions at hand for both F− +
CH3Y [Y=Cl,I] reactions8,13 we
have a unique starting point to obtain statistically accurate
spatial probability distributions. To
shed light on the effective dynamics of these reactions, the
trajectory orthogonal projection
(TOP) method has been applied to the entrance channel of all the
reactive SN2 trajectories by
imposing the following constraints on the internal coordinates
of CH3Y: rC-I < 3.5 Å, and max(rC-
H) < 2.5 Å in order to avoid the interference with the SN2
exit-channel and the proton-abstraction
pathway. (Note that the barrier of halogen abstraction is
usually much higher than the maximum
collision energy in this study.) In Fig. 2 the normalized
spatial probability of the attacking Nu−
around CH3Y (Y=Cl,I) is shown at collision energy of 1 kcal
mol−1. On the one hand, the
distributions corresponding to the two reactions bear
similarities in the back-side region, where
both reactions show a characteristic peak which centers (red
spot) on the C3 axis of CH3Y
[Y=Cl,I] at a Nu−-I distance equal to the sum of rI-C,eq and
rC-Nu,eq distances in the IH3C--Nu−
prereaction ion-dipole complex. As also expected, a higher
probability region emerges on the 2D
map in close proximity of the H atom as an indicator of the
extensive YH2CH--Nu− H-bonded
complex formation. It is noteworthy that the Nu− probability
distribution in the BSC region is
broader in case of the F− + CH3I reaction, which is consistent
with the larger bmax values for this
SN2 reaction.12,13 This increased chance for energy
redistribution between the inter- and
intramolecular modes of the pre-reaction complex may be a
principal recipient of the more
pronounced indirect nature of the F− + CH3I SN2 reaction. On the
other hand, in the front-side
region the difference in Nu− spatial distributions is striking.
The F− + CH3I reaction features a
prominent peak corresponding to the position of F− in the
F−--ICH3 front-side ion-dipole
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complex; however, in case of the F− + CH3Cl reaction the spatial
distribution of F− is completely
isotropic in the front-side region. These findings are in line
with the characteristics of the
interaction potentials. The probability distributions for both
reactions are qualitatively the same
up to a collision energy of 15.9 kcal mol−1 (see Fig. S3-5). At
higher collision energies (Fig. S6)
the reaction is mainly direct suppressing the orientation
effects, thus only those reactants lead to
products, which start with back-side attack. Moreover, the
dominant direct roundabout
mechanism hinders the formation of ion-dipole and H-bonded
complexes, and results in
backward scattered products.12,13
An approach for investigating the time-scale of nucleophile
capture is to consider the fraction of
the trajectory spent in the FSC region.22 Considering the shape
of the interaction potential, as
well as the spatial distribution of the nucleophile, the life
time of the individual capture events is
calculated from the trajectory integration times in the
�Nu�Y
< 0 region, where �Nu�Y is the distance
of the trapped Nu− from the Y halogen atom after orthogonal
projection to the {Y,C} line. We
should emphasize, that our definition for the front-side region
is not limited to the close
proximity of the Y halogen atom, because after inspection of
many trajectories we had to realize
that the trapped trajectories span a long-range region of the
configurational space. Nevertheless,
the exact separation of the temporarily and strongly trapped
trajectory segments is not
straightforward. Although, this difficulty may eventually be
overcome by analysing the residence
time of the F− ion in the FSC region. As seen on Fig. 3a and 3b,
the life time distribution of
individual front-side complexation events features two regions.
Up to 4 and 2 ps for F−--ICH3
and F−--ClCH3, respectively, the short-lived transient complexes
are represented by high
probability peaks, but the probability instead of dropping to
zero it extends to very large life
times, denoted with tFSC,max, especially in case of the F− +
CH3I reaction. These long-lived,
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strongly trapped complexes have an isotropic life time
distribution up to tFSC,max (not shown on
the graphs) and show little Ecoll dependence at moderate
reactant translational energies. To track
the differences in life time distributions for the two systems
we performed QCT simulations with
Cl of mass 127 a.u. (corresponding to I) using the F− + CH3Cl
PES.23 As predicted before,9 the
mass-scaling has only minor effects on the life time
distribution and tFSC,max, thereby
underpinning the role of the interaction potential. Considering
the partitioning of the total life
between short-lived and long-lived FSCs the two reactions differ
dramatically. Interestingly, the
strongly trapped F− + CH3I trajectories constitute only about 1%
of the FSC events; but it is truly
impressive that they accumulate ~35% of the total FSC life time
at a collision energy of 1.0 kcal
mol−1 and ~55% at 15.9 kcal mol−1 considering the back-side and
front-side attack trajectories
together. Since the reaction becomes more direct at higher
collision energies the fractions of life
time corresponding to BSA trajectories are also increased. In
case of the F− + CH3Cl reaction the
fraction of long-lived trajectories is almost negligible and the
Ecoll dependence of the life time
fractions shows similar trend to the F− + CH3I system.
Representative trajectories presented in Fig. 4 hold evidence
for formation of the front-side
intermediate complex on the example of the F− + CH3I reaction at
Ecoll = 2 kcal mol−1. As seen
on panel a, even trajectories starting with back-side attack
(red arrow) can easily get around the
polyatomic reactant, CH3I and after spending a short time in the
front-side well can lead to
reactive event. Another typical trajectory is shown on panels b
and c projected to the
{I,C,H(red)} plane and to the plane perpendicular to
{I,C,H(red)}, respectively. Here, the F−
nucleophile approaches CH3I from the halogen side and it is
immediately captured in the front-
side well for 42.1 ps. Note that this residence time is
approximately 20 times larger than the
trajectory integration time of a complete rebound or stripping
process and it is comparable with
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the time-scale of the indirect mechanism.8,12,13 After
dissociation of the F−--ICH3 intermediate
complex, the F− ion leaves the front-side region being trapped
for a short time in the back-side
region of the pre-reaction well. Once its relative orientation
to the permanent dipole becomes
appropriate, the substitution event can take place by
simultaneous C-F bond formation and C-I
bond rupture.
Although, front-side intermediates assume a non-reactive
ion-dipole orientation, the dynamics of
SN2 reactions at low collision energies is partially controlled
by the nucleophile capture in the
front-side region of the pre-reaction well. At the high
collision energy regime (> 35 kcal mol−1)
the probability to find front-side complexes is lower, because
the FSC formation is suppressed
leading to shorter life times. We can conclude that FSC
formation is a principal component of
the indirect mechanism. It will be of great interest to
investigate the effect of mode-specific
excitation on the migration of the Nu− in the pre-reaction well
and quantum dynamics studies are
also highly desired to analyse the resonant states in the
front-side region.24 In a wider context, the
present proof of principle application of the trajectory
orthogonal projection (TOP) method is a
solid starting point to reveal reaction pathways and thoroughly
understand the effective dynamics
of the fundamentally important SN2 reactions using dynamics
mapping.
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Figure 1. Structure and energetics of front-side complex (FSC)
minima. (a) Structural
parameters and energies relative to the F− + CH3Y(eq) [Y=Cl,I]
reactant asymptote obtained at
the CCSD(T)-F12b/aug-cc-pVTZ(-PP) level of theory (b-f) Entrance
channel interaction
potential energy scans of F− + CH3Y(eq) [Y=Cl,I] performed at
the CCSD(T)-F12b/aug-cc-
pVDZ(-PP) level of theory; the energies are relative to the F− +
CH3Y(eq) reactant asymptote.
(b) Definition of the potential energy surface scan. The
structural parameters and relative
energies of Nu− + CH3Y [Nu=F,Cl,Br,I; Y=Cl,Br,I] FSC minima are
given in the Supporting
Information.
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Figure 2. Spatial probabilities of the F− nucleophile around
CH3Y [Y=Cl,I] on the reactant side
of the F− + CH3Y → CH3Y + F− [Y=Cl,I] substitution reactions at
the collision energy of 1 kcal
mol−1 using all the trajectories, which satisfy the following
conditions: rC-Y < 3.5 Å and rC-H < 2.5
Å. Normalized distributions were obtained by 1D (a,b) and 2D
(c,d) trajectory orthogonal
projection (TOP) to the {C,Y} line and to the {Y,C,H(red)} plain
as indicated by the structures,
respectively, combined with the standard Histogram Analysis
method.21 The front-side and back-
side complex regions of the configuration space are denoted with
FSC and BSC, respectively.
Further spatial probability distributions at collision energies
of 4.0, 15.9, 35.3 and 50.0 kcal
mol−1 are given in the Supporting Information.
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Figure 3. (a,b) Front-side complex life time distributions for
the F− + CH3Y [Y=Cl,I] SN2
reactions at different collision energies. The life time is
calculated from the trajectory integration
time spent by the F− nucleophile in the front-side region
defined as �F�Y< 0, where �F�
Y is the
distance of F− from the Y leaving group after TOP. (c,d)
Front-side complex life time fractions
split into the individual contribution of trajectories starting
with front-side attack (FSA) and
back-side attack (BSA). The FSA and BSA trajectories are
distinguished based on the initial
attack angle defined as the angle between the C-Y vector and the
velocity vector of CH3Y at t =
0. Furthermore, the FSA and BSA are split into the contribution
of short-lived (transient) and
long-lived (strongly trapped) FSC trajectories. The latter ones
are characterized by a life time
larger than 2 and 4 ps for Y=Cl and Y=I, respectively.
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Figure 4. Representative trajectories in the entrance channel of
the F− + CH3I SN2 reaction at
collision energy of 2 kcal mol−1 exhibiting front-side complex
(FSC) formation. The dynamics
maps were obtained by projection to the planes indicated by the
structures on each panel using
the 2D TOP method (see text and also Figure 2). (a) Transient
short-lived FSC trajectory starting
with back-side attack, and showing F− trapped in the FSC region
of the pre-reaction well for 0.6
ps before the reactive SN2 event. (b,c) Two projections of the
same trajectory starting with front-
side attack, and featuring long-lived intermediate FSC; the F−
nucleophile is strongly trapped for
42.1 ps before the reactive substitution event.
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COMPUTATIONAL METHODS
All the ab initio electronic structure computations (geometry
optimizations, frequency
computations, and potential energy surface scans) were carried
out by the Molpro 2015.1
program,25 except the computation of the molecular orbitals and
the Natural Bond Orbital (NBO)
population analysis, which were done with the Gaussian 09
program package.26
Quasi-classical trajectory (QCT) computations for the F− + CH3Y
[Y=Cl,I] reactions were
performed with our in-house computer code using the recently
developed analytical ab initio
potential energy surfaces.8,13 The vibrational ground state of
the polyatomic reactants CH3Y
[Y=Cl,I] was prepared by normal mode sampling and their
rotational temperature was set to 0 K.
The initial orientation of CH3Y [Y=Cl,I] was randomly sampled
and the distance between the
centers of mass of the reactants was (x2+b2)1/2, where b is the
impact parameter and x was 30/40,
20/30, 20/30, 20/20 and 20/20 bohrs for Y=Cl/I at collision
energies of 1, 2, 4, 10 and 15.9 kcal
mol−1, respectively. Trajectories were also run at collision
energies of 35.3 and 50 kcal mol−1 for
the F− + CH3I reaction with x set to 20 bohrs. b was scanned
from 0 to bmax, which is the
maximum value of b, where any reactive event can occur, with a
step size of 0.5 bohr, except at
collision energies of 35.3 and 50 kcal mol−1, where a smaller
step size of 0.125 bohr was
employed in order to get improved statistics for the spatial
distributions of the nucleophile. At
each b 5000 trajectories were propagated, resulting in more than
2 million trajectories in this
study. We also performed dynamics simulations for the
mass-scaled reaction F− + CH3Cl’ by
setting the mass of Cl’ to 127 a.u. and using the PES of F− +
CH3Cl.23 For the exothermic F− +
CH3Y → CH3Y + F− [Y=Cl,I] substitution reactions the zero-point
energy (ZPE) violation is
negligible, thus the QCT product analysis considered all the
reactive trajectories. The spatial
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distributions of the F− nucleophile were obtained by the
trajectory orthogonal projection (TOP)
method combined with the standard Histogram Analysis
procedure.
ASSOCIATED CONTENT
Supporting Information
Structures and relative energies of the Nu−--YCH3 [Nu=F,Cl,Br,I;
Y=Cl,Br,I] front-side
complexes (Figure S1); Molecular orbitals and atomic charges of
the F−--YCH3 [Y=Cl,I] front-
side complexes (Figure S2); Spatial probabilities of the F−
nucleophile around CH3Y [Y=Cl,I] on
the reactant side of the F− + CH3Y → CH3Y + F− [Y=Cl,I]
substitution reactions at different
collision energies (Figures S3-6); Classical energies of the
Nu−--YCH3 [Nu=F,Cl,Br,I;
Y=Cl,Br,I] front-side complex minima (Table S1); Harmonic
vibrational frequencies for front-
side complex minima (Table S2)
AUTHOR INFORMATION
Corresponding Authors
*E-mail: [email protected] (I.S.), [email protected]
(G.C.).
Notes
The authors declare no competing financial interests.
ACKNOWLEDGMENT
I.S. was supported by the UK EPSRC Fellowship EP/N020669/1. G.C.
was supported by the
Scientific Research Fund of Hungary (PD-111900) and the János
Bolyai Research Scholarship of
the Hungarian Academy of Sciences. We acknowledge the National
Information Infrastructure
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Development Institute for awarding us access to resource based
in Hungary at Debrecen and
Szeged.
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